goalie4life

Nah. The fact that the email was sent anonymously--and from a fake account, no less--means that it's not worth dignifying or thinking about. 
If we're going to teach our students anything about post-college life, we have to stress that integrity is key. If you can't make a complaint in person or under your real name, you can't expect an audience to respond to your problems. You can't expect people to drop everything to come and troubleshoot your issues when you refuse to air those issues under your real identity.  
The OP used their computer to fact check the lecture and check work-related email. That does not qualify as someone "putting your priorities ahead of your students'." I actually think it's telling that you immediately jumped to the conclusion that the OP is somehow abusing their power or shirking their duties as a TA. If laptops are permitted in the lecture, then the TA can certainly use them for this purpose. 
Moreover, TAs are not in the same position as their undergrads. They come in already knowing the material, for the most part, and they're there to grade papers and lead recitation sections. They answer to the professor, not to the students. The students are not the TA's boss. As long as the TA is fulfilling the duties that the program and professor specify, then they are doing what they're supposed to do. Students do not get to dictate how a TA should comport him or herself during lecture, just as they do not get to tell TAs what to wear or where to sit.  
And you have absolutely no cause to apply this "crisis" to anything that the OP has done. Nowhere in their original post did the OP reveal that they think interacting with undergrads is an "annoyance." In fact, the OP came to this forum to ask, in good faith, how they should proceed. Nothing in the original post should allow you to assume that they conduct themselves in a manner that's anything less than professional with their students. 
Moreover, your assumption--that this TA's interaction with students--is somehow deepening the gulf between undergrads and professors--is pretty unsubstantiated. You're implying that this undergrad--and perhaps others--will somehow be "lost" to the history profession because of the OP's laptop use. Well, I hate to break it to you, but anyone who sends an anonymous and petty email to their history TA about laptop use--perfectly harmless laptop use at that--is probably not enamoured of the history profession anyway. I'm guessing we didn't just lose another potential history major because of the OP's laptop. 
More significantly, I'd like to see some sources that substantiate your claim that academic history is "in crisis" as a discipline precisely because of poor teaching, poor relationships with undergraduates, and mistreatment of undergraduates by TAs. Because, as someone who also works in the humanities, I have to tell you that the humanities are in crisis for reasons that have very little to do with our teaching. Students aren't going to college to major in humanities anymore for economic reasons. Universities aren't admitting as many humanities students because they're trying to build STEM and business schools. Blaming professors and TAs for the crisis in the humanities seems like another way to diminish the work that we do, and a convenient passing-of-the-buck to the people who deserve it the least. 
Since the email was anonymous, I'm not sure how this would work. Should the OP reply to the anonymous email and ask them to come to office hours and unveil themselves? Or should they tell the entire class what happened and ask the anonymous emailer to please come forward? That seems like a lot of energy wasted on a student who couldn't be bothered to lodge a complaint under their own name. TAs have their own work to do. Devoting so much time and energy to a rather minor (and probably trollish) complaint is counterproductive. 
Again, I'm not sure what this conversation would accomplish. If the point isn't to apologize, then I'm not sure what purpose such a meeting would serve. Are we validating the undergrad's feelings? Are we sending them a message that you can go ahead and send a petty and anonymous email and get someone to rearrange their afternoon to deal with your minor complaint?
Honestly, I think most professors would be utterly mystified to get this kind of memo ... about a student who sent an anonymous email to a TA because the TA was fact-checking during a lecture. Uh, most of my professors/bosses would have asked me if I had too much time on my hands or if I was finished with my dissertation already. 
Moreover, TAs and professors aren't in "customer service." Our students are not customers, and we're not trying to manage risk. 

I'm going to disagree respectfully with the other responses on two points.
First, there's nothing out of line in the student's email. He/she made an observation that was partially accurate and expressed a preference. The fact that the feedback was offered anonymously is not a big deal. (Disclosure: when I T.A.-ed, I offered anonymous feedback forms.)
Second, the student's observation was partially accurate. The grant and the email were relevant to your interests as a graduate student, they were irrelevant to your job as a teaching assistant. By focusing on other things, you may have missed opportunities to do your job more effectively. The lecturer may have gotten something wrong, or left the students scratching their heads in confusion, or nodded their heads in thoughtful silence, or have missed the point--all of these scenarios might have been opportunities for you to support your boss and, more importantly, your students.
IMO, the facts that the student isn't one of yours, that you were in policy, and that a professor also uses his laptop do not trump the fact that you put your priorities ahead of your students'. The fact that you can do so does not mean that you should. (Your point that you'd never do in your own class what you did in the lecture is telling. [Disclosure #2: I got my B.A. from where you are now and that level of nuance...yikes...that's a can of worms you don't need to be carrying in your backpack.])
Here's the thing. Academic history is a profession in crisis. Part of the crisis is due to the growing distance between professors and their students (undergraduate and graduate). Another part is due to the fact that graduate students often treat interaction with undergraduates as an annoyance rather than as an opportunity to build public confidence in the craft and its practitioners.
The following is worth exactly what you're paying to read it.
Were I in your situation, I would either position myself so that no one could see what I was doing on my laptop or I would restrict my laptop use to tasks directly related to the class. (FWIW, in lectures, I generally stood in a location where I could see the lecturer and most of my students while taking notes.) 
Depending upon my frame of mind, I'd either offer an invitation to the student to talk it over in person or I'd not acknowledge the email. 
In any conversation with the student, I would acknowledge but not apologize for my laptop use. I would make no promise whatsoever or say anything that could be misconstrued as one. I'd then write a memo of the conversation and email it to my boss. (Disclosure #3: I currently work in the private sector in an industry where it is all about customer service...and risk management.) I would then treat myself to something with caffeine, vent colorfully about the whole thing, and then get back to the stacks. Where I'd do more venting.*
Going forward, if you don't want to receive anonymous emails, distribute a sign up sheet on which students will put their school email addresses. Explain that you will only accept messages from accounts ending @yoursschool.edu and everything else is going into the trash. Say it's because of the latest disclosure about Yahoo! or the FBI raid. Before using this tactic, please make sure that it is permissible with your boss, your department, and in policy. If you can't make the transition this semester, see what you can do for next semester.
 
_______________________
*A true story. Early one semester, I received some blistering criticism on an anonymous response form. Livid, I spent some time trying to figure out who wrote it. I then went to my boss's office and vented. "The worst thing about it," I sputtered, "is that it's true." He laughed, I left ...and went back to trying to figure out who wrote it. I did. And I also made the adjustment the student suggested. Live and learn. Or something.
 
 

@rising_star, I'm not quite sure why you're replying in such a defensive and condescending manner here. I agreed with most of what you said and just had a few nitpicks. But we're talking about conference presentations here, not the virtues of collaborative scholarship. If you want to talk about collaborative scholarship, I'm guessing the research forum would be a better place? But here we're discussing the value of conferences for early career grad students. I don't doubt that you're very good at what you do. But you represent just one institution (or class of institutions, I suppose), and you're not in English, and you're not on every hiring committee. If we're going to go to qualifications, I was on several search committees as a graduate student, and I too am currently a faculty member at a much different type of institution from the one where I received my degree, and I've been on the job market very recently and have gotten a TT job. I'm familiar with P&T guidelines (as someone striving to fulfill them currently), and your recommendation just doesn't apply to the situation we're discussing here. Like, it's great that your institution encourages collaboration. It's certainly not the case everywhere. In fact, English faculty at all kinds of institutions these days are striving to publish a book for tenure--even when a book is not required. It's quickly becoming the standard, though, because the discipline is so talent-rich (you have people working at teaching-focused institutions who in the past would have easily been hired at an R1). This has changed the topography of English scholarly expectation quite a bit.
But this conversation isn't about scholarly collaboration and people getting tenure. It's about people trying to get into graduate school and wondering what conferences will do for them.  As I said previously, graduate students in English have only a limited time to get through a program. Publishing a solo article is A MUST. You have to get your name out there before hitting the job market, and a co-authored essay probably won't do that for you. Are there exceptions? Probably. Do I know people who have co-authored papers and gotten jobs? Of course. Was the co-authored article the only thing they produced? Absolutely not. Can a co-authored article help you if it's your second or third article rather than your first or only, and you already have a scholarly footprint? Probably, but it depends on its quality and the level of your involvement. However, it still does not carry the weight on the job market that a solo project does, and this is why many DGSs and advisors discourage it. When you only have five years of funding to get through, you need to prioritize your time to get that solo article out, because that is what will get you an interview. That's the thing: writing articles takes time, even co-authored articles. They are an incredible time suck. And I recommend that graduate students try to get the maximum return on their investment by publishing two peer-reviewed articles (usually one that's published or about to be published when one is on the job market and then one that appears soon after one gets hired--that's still ideal, even if the hiring crunch has made it more difficult to have a job by the time that second article comes out).
If you've already published your two articles and now want to co-author a third, why not. It's another notch in the belt. It probably isn't going to light the world on fire, but it's a line on a CV. But this conversation should not be about co-authorship. It's about conferences. And this is still my advice about conferences: If a scholar approaches you at a conference and wants to co-author a paper with you, great! Flattering! But is this article something you're already doing on your own? Do you already have an article in the pipeline and another one under review or soon to be under review? How much funded time do you have left? How much more of your dissertation do you have to write? How much time do you think this project will take? Depending on the answers to these questions, co-authoring a paper might or might not be a great idea. Get that information together and take it to your advisor to see what they say. 
(And anecdotally, and somewhat related to this conversation: I was approached at a conference five years ago by a famous scholar who wanted me to turn my conference paper into a book chapter for a collection. I passed on the offer, submitted the article to a journal, and later won a prize for that article, which was instrumental in my success on the job market. Turning down the edited book collection actually paid off well.) 
They need to just put it out there. In the social sciences you consider co-authoring papers to be part of one's training? Well okay, there's a difference in disciplines here. In English programs we still believe that a valuable part of one's training is to tell someone to finish the article, attach it to an email, and send the damn thing.  

Sure; but is keeping people out of a 5-year-long dead end bad or good?
I guess I'm struggling to express my thinking. In my understanding, this all goes back to the question that, if a PhD program consistently cannot graduate employable specialists, why does it exist? It should be a fully-funded master's that prepares people for entry to programs that can, or else gives them 2 years to experience professional scholarship and conclude it's not for them. Given there are major structural issues for why that will never happen, is it still immoral to treat these programs as funded master's? I don't know; but at least it seems to me efficient.
My other qualm is that there is a lot of people are spiritedly defending these institutions and The Community, but these institutions are constantly and brutally shafting graduate students and junior faculty, and the more junior you are, the harder you get shafted. The "wasting money that could've gone to qualified applicants who would get the PhD" argument doesn't really work for me, because if all your PhDs end up adjuncting six introductory classes or in the nebulous miasma of "alt-ac" rather than doing what they've trained for the better part of a decade to do, in my understanding that's still wasted money. If the department loses PhD funding because they can't retain enough PhDs - well, maybe they should. Maybe that will push them to offer respectable master's options, which is what is actually needed, rather than having people pledge their lives to the void. 
I'm not arguing that OP will be shooting themselves in the foot if they get a reputation for being opportunistic. I'm just arguing for clemency towards people who face OP's choices.

Controversial opinion: I'm not sure that what OP is proposing is so reprehensible. Realistically, people need to attend the top programs in order to have a chance at a job, but even becoming competitive for admissions to top programs is logistically difficult and costly for anyone who's changing fields, who comes from a low-ranked undergrad, or who is simply ill-acquainted with how academia works. So what should those people do? Take out student loans for a useless MA in the humanities? Give up and get an office job? One is a stupid financial decision (and one consistently recommended against on this board) and the other is contributing to making academe a club for the wealthy. 
On the other hand, you have low-ranked programs that graduate their PhDs into no chance of a job, and know that this is the reality, where professors will outright tell you that, if you're getting a PhD here, you shouldn't be getting a PhD. Yeah, agreeing to attend a program for 5 years and quitting once you've found something better can be construed as a breach of trust - but taking 5+ years of people's lives (and exploiting their vastly underpaid TA labor so you don't have to create tenure lines to support your undergraduates) and then pushing them out to a world where they have a better chance of winning at slots than getting TT? When the contract is so broken on the one side, I don't know that people on the other side should be held to pristine standards.
I understand that people feel very emotional about the kind of plan OP proposes, because academia is more than just a job, but it's much easier to reflexively shit on the little person than to recognize that they are operating within the confines of a broken system.